Nonlinear Optimization Algorithms for Large-Scale and Nonsmooth Applications

适用于大规模和非光滑应用的非线性优化算法

• 批准号: 1016291
• 负责人: Frank Curtis
• 金额: $ 11万
• 依托单位: Lehigh University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2010
• 资助国家: 美国
• 起止时间: 2010-07-01 至 2013-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1016291&HistoricalAwards=false
• 关键词: Nonlinear; Optimization; Algorithms; Large; Scale

The investigator, his colleagues, and his students study the development, analysis, and implementation of algorithms for large-scale PDE-constrained and nonsmooth optimization. The novelty of the work in both of these frameworks is that in each case the investigator and his group are finding powerful ways in which the most advanced methods for nonlinear programming can be enhanced and broadened to remain effective for application areas in which they have previously been inefficient or inapplicable. In the context of large-scale PDE-constrained problems, such as those in optimal design, parameter estimation, and image registration, this is being achieved by removing the need for the factorization of matrices and allowing for inexactness in the solution of large-scale linear systems, while still guaranteeing convergence to a solution point. In the context of nonsmooth applications, such as those in compressed sensing and robust stability and control, this is being achieved by enhancing leading algorithmic frameworks through a process of gradient sampling, allowing for a loosening of the assumption that the problem functions are differentiable everywhere. These works in these fields tie together algorithms and computational techniques from diverse areas, and both numerical methods and convergence theory are being provided.The broader impact of this project is that it advances pencil-and-paper engineering ideas to the point where they can be implemented in high-performance computing software and are able to solve challenging problems in the design and analysis of complex systems. For example, there is a high demand for optimization tools such as these in healthcare, particularly in the area of cancer treatment and therapy. By providing doctors and medical technicians with novel computational tools, they will be able to optimally administer hyperthermia treatment in a manner that takes into account the inner complexities of the human body, such as blood flow. They will also be able to effectively and adaptively design plans for radiation therapy that minimize damage to healthy -- and often critical -- tissue near the target area(s). Amazingly enough, these same computational tools can also be employed in medical image registration, aiding medical professionals in the detection of irregularities over time and between different (e.g., PET, CT, MRI) scans. The goal in all of these areas is to provide the user with sophisticated software that can answer, in real-time, difficult questions such as "What is the optimal way of administering this radiation?" and "Is there anything in this image that has changed or is cause for alarm?"

研究人员，他的同事和他的学生研究了大规模PDE受限和非平滑优化算法的开发，分析和实施。 在这两个框架中，这项工作的新颖性是，在每种情况下，研究人员及其小组都在寻找有力的方法，即可以增强和扩展非线性编程的最先进方法，以对以前效率低下或不适用的应用领域保持有效。 在大规模PDE约束的问题的背景下，例如最佳设计，参数估计和图像注册的问题，这是通过消除矩阵的分解并允许在大型线性系统解决方案中不精确的情况来实现的，同时仍然保证融合解决方案点。 在非平滑应用程序的背景下，例如压缩感测和稳健的稳定性和控制的应用程序，这是通过通过梯度采样的过程来增强领先的算法框架来实现的，从而使问题函数在无处不在的情况下允许放松假设。 这些在这些领域中的作品将算法和来自不同领域的计算技术结合在一起，并提供了数值方法和收敛理论。该项目的更广泛的影响是，它可以将铅笔和纸工程思想推进到可以在高表现计算软件中实现的地步，并能够在复杂系统的设计和分析中解决挑战性问题。 例如，在医疗保健中，尤其是在癌症治疗和治疗领域，对诸如此类的优化工具的需求很高。 通过为医生和医疗技术人员提供新颖的计算工具，他们将能够以一种考虑人体内部复杂性（例如血液流量）的方式来最佳地治疗高温治疗。 他们还将能够有效，自适应地设计辐射疗法的计划，以最大程度地减少目标区域附近健康（且通常是关键）组织的损害。 令人惊讶的是，这些相同的计算工具也可以用于医学图像注册中，这有助于医疗专业人员随着时间的流逝以及不同（例如PET，CT，MRI）扫描之间的不规则检测。 所有这些领域的目标是为用户提供精致的软件，这些软件可以实时回答诸如“管理此辐射的最佳方式”之类的困难问题？和“此图像中有任何变化或引起警报的东西？”